Diagnóstico y Determinación de necesidades

In this chapter, I have presented a dynamic general equilibrium model to explain the role of overhead labour in skill-biased technological change. In the model, it is the increasing ratio of the xed labour input to the variable labour input that increases the demand for skill. It is because the overhead labour is assumed to be biased towards non-production workers, and non-

production workers are usually those with a higher education level.

This model presents several predictions, which dier from the standard SBTC theory. Firstly, this model predicts that the employment share of white-collar workers interacts with the market structure. Evidence is pro- vided suggesting that those industries with higher mark-up are likely to have higher employment shares of white-collar workers.

Secondly, it is predicted that there is an upper bound to the skill-biased change. Since the rms can pay for the xed labour input only if the price exceeds the marginal cost, the wage-bill share of white-collar workers cannot increase indenitely. Therefore, it is predicted that the growth of inequality between the white-collar workers and the blue-collar workers is likely to experience a slowdown in the long run.

Thirdly, while the increase in the employment share of non-production workers is expected to increase measured labour productivity through the composition eect in existing literature, this model predicts that the com- positional eect on the measured productivity will be negative. Therefore, this model's prediction is consistent with such puzzling empirical facts as the rapid development of skill-biased technology coupled with stagnant productivity in the 1980s and the opposite pattern in the 1990s, wherein the slow down of skill-biased technological change was coupled with the resurgence of labour productivity growth.

Appendix. About mark-up ratio data

The mark-up ratio data comes from Oliveira Martins et al. [1996], who utilized Roeger [1995]'s method. Roeger [1995] utilises the gap between TFPs measured by dierent methods. Typically, TFP is estimated by calculating Solow residual as below:

SR= ∆q−α∆l−(1−α)∆k (1.11)

Here, SR refers to Solow residual, and α is the share of labour income

in the output. ∆l, ∆k, ∆q are the dierences in the logs of labour input,

capital input and output. The contribution of each factor in production is equal to its income share under the assumption of perfect competition.

However, Roeger [1995] showed that TFP can also be estimated using a price-based Solow residual. It is dened by the dierence between the increase in the weighted average of the factor price and the increase in the price of output as below:

SRP =α∆w−(1−α)∆r−∆p (1.12)

Here, SPR refers to price-based Solow residual. ∆w,∆r,∆pare the dif-

ference in the logs of wage, rental rate of capital and output price. When there is a positive technology shock, the output price rises less than the increase in the factor prices as the factors are consumed less due to the productivity improvement. In theory, under the assumption of perfect com- petition, TFPs estimated by both methods should be the same in theory. However, they are rarely identical in practice.

measure of labour's contribution to production under imperfect competi- tion. The exact contribution of labour is equal to its income share in the marginal cost, which is lower than the price. Therefore, labour's income share of output underestimates the contribution of labour and overesti- mates the contribution of capital under imperfect competition. As a re- sult, both Solow residuals are biased, but in dierent directions. From the gap between these two types of Solow residuals, the mark-up ratio can be estimated as below:

SRt−SRPt=B∆xt+ut (1.13)

∆xt= (∆yt−∆kt) + (∆pt−∆rt)

Here, B is the Learner index dened as B = P −M C

P , or B = 1−

1

µ,

whereµis mark-up ratio. The mark-up ratio is derived by estimating B in

equation (1.13). However, Oliveira Martins et al. [1996] modify Roeger's method to incorporate material inputs in equation (1.13). The estimation equation used in Oliveira Martins et al. [1996] is:

∆yt =B ·∆xt+εt (1.14)

where,

∆yt = (∆q+ ∆p)−α·(∆l+ ∆w)−β·(∆m+ ∆pm)−(1−α−β)·(∆k+ ∆r)

∆xt= (∆yt−∆kt) + (∆pt−∆rt)

Oliveira Martins et al.(1996) also adjust for the eect of indirect taxes on the estimated mark-up as below:

µ= µ

e

1 +τ

Here, µe_{is the estimated mark-up, andτ is indirect tax rate. Estimated}

mark-up ratios from Oliveira Martins et al. [1996] are shown in Table 1.1. The industrial classication system they use in Oliveira Martins et al. [1996] is ISIC rev.2. Data on payment, capital stock and material cost are based on NAICS 97 classication in this study. Therefore, only ISIC rev.2 in- dustry groups with a clear correspondence to NAICS 97 classications are used for estimation.

Table 1.1: The mark-up ratio in the US manufacturing, 1970-1992

Sector name (ISIC rev.2) Sector (Naics 97) mark-up Food Products 3112∼ 311000∼312000 1.05 Beverages 3130∼ _{- -} Tobacco products 3140∼ ₃₁₂₂₀₀∼_{313000 1.56} Textiles 3210∼ ₃₁₃₀₀₀∼_{313000 1.08} Wearing apparel 3220∼ 315000∼316000 1.10 Leather products 3230∼ 316000∼321000 1.08 Wood products 3310∼ ₃₂₁₀₀₀∼_{322000 1.22} Furniture 3320∼ ₃₃₇₀₀₀∼_{339000 1.06} Paper products & Pulp 3410∼ ₃₂₂₀₀₀∼_{323000 1.13} Printing & Publishing 3420∼ 323000∼324000 1.19 Industrial chemicals 3510∼ 325130∼325400 1.18 Drugs & Medicines 3522∼ ₃₂₅₄₀₀∼_{325500 1.44} Chemical products 3529∼ ₃₂₅₅₀₀∼_{326000 1.26} Petroleum reneries 3530∼ _{324110 1.03} Petroleum & Coal products 3540∼ 324121∼324199 1.11

Rubber products 3550∼ - -

Plastic products 3560∼ ₃₂₆₀₀₀∼_{326200 1.07} Pottery & China 3610∼ ₃₂₇₀₀₀∼_{327200 1.09} Glass products 3620∼ ₃₂₇₂₀₀∼_{327300 1.17} Non-metal products 3690∼ 327300∼331000 1.18 Iron & Steel 3710∼ 331000∼331300 1.10 Non-ferrous metals 3720∼ ₃₃₁₃₀₀∼_{332000 1.14} Metal products 3810∼ ₃₃₂₀₀₀∼_{333000 1.09} Oce & Computing mach. 3825∼ ₃₃₄₀₀₀∼_{334200 1.54} Machinery & Equipment 3829∼ 333000∼334000 1.06 Radio, TV & Comm. equip. 3832∼ 334200∼334300 1.40 Electrical apparatus 3839∼ _{- -} Shipbuilding & Repair 3841∼ _{- -} Railroad equipment 3842∼ _{- -} Motor vehicles 3843∼ 336000∼336400 1.09 Motorcycles & Bicycles 3844∼ _{336991 1.13}

Aircraft 3845∼ _{- -}

Other transport equipment 3849∼ _{- -} Professional goods 3850∼ - - Other manufacturing 3900∼ 339000∼340000 1.08

Chapter 2

White-collar employment and

rm scale

2.1 Introduction

There has been a secular rise in the share of white-collar workers, and this is usually attributed to the aggregate technological change. For example, the IT revolution, which had widespread eects on the economy, is considered to be the key factor driving skill-biased technological change. However, the pattern appears very dierent at rm level, especially at high frequency. In this chapter, rm level high frequency variation in the employment share of white-collar workers is empirically studied using the ARD rm level database on UK manufacturing industries.

A considerable level of heterogeneity between rms is found. Around 40% of rms decreased the employment share of white-collar workers from the previous year, although the aggregate share of white-collar workers was rising. At rm level, a large portion of high-frequency changes in the white-collar employment share cannot be fully explained by aggregate

technological change, given that it is unrealistic to expect technology to deteriorate for such a large portion of rms1_{, accounting for around 40}

percent of total rms. As Dunne et al. [1996] have pointed out, there are unobservable factors, seemingly not related to technology, which generate high-frequency variation in white-collar employment share at rm level. This study suggests that the change in rm scale is one of those factors.

The level of production and employment uctuates more at rm level than at aggregated level. I nd that the labour demand for white-collar and blue-collar is not homothetic, so the change in rm scale aects the com- position of employment as well as the scale of employment. There has been literature on the eect of rm size on a wide range of economic variables including rms' survival rate (Baldwin and Raquzzaman, 1995; Disney, Haskel and Heden, 2003), productivity (Leung, Danny, Meh, Cesaire and Terajima, Yaz, 2008), earning or job creation(Hijzen, Upward and Wright, 2010), but it is relatively rare to focus on its eect on relative demand for skilled (white-collar) workers.

In this chapter, the share of white-collar workers is found to be positively correlated with rm size across the cross-section. However, it is also found that the change in the share of white-collar workers is negatively correlated with the change in rm scale. So, the main aim of this study is to investigate why the positive relationship between white-collar employment share and rm size in the cross-section dimension is reversed in the time dimension.

As in the rst chapter, it is also assumed that white-collar workers constitute xed labour input. However, two assumptions in the previous chapter are relaxed here: some of the white-collar workers are variable in-

1_{This question is somewhat related to another question about RBC theory that how}

put, and dierent products have dierent levels of xed white-collar labour input. As it is assumed that the employment share of variable white-collar labour to blue-collar workers is homothetic, the non-homothetic property is supposed to come from the existence of xed white-collar labour.

The empirical nding that the adjustment of white-collar employment is lumpier than the blue-collar workers is consistent with the hypothesis that white-collar labour is partially a xed input. The employment of white-collar workers changes less frequently than that of blue-collar work- ers. However, when it changes, it changes more. This might be explained by the partial xity of white-collar labour input. For example, the rm's em- ployment of xed labour is not supposed to change unless the rm changes its product variety to another one with a dierent minimum required level of xed labour input. However, once the rm decides to change the product into another one with either higher or lower required level of xed labour input, the employment of white-collar labour changes discontinuously, gen- erating lumpy adjustment.

If a rm produces a more sophisticated product, which requires a higher level of xed white-collar labour input, the rm is more likely to be large in size. Moreover, higher level of xed input limits the number of rms and increases the price-cost mark-up. Therefore, rms with higher xed labour input also would also show a higher employment share of white-collar workers. Therefore, the rm size is positively correlated with white-collar employment share as both of them are positively correlated with the size of xed white-collar labour input, which is unobservable.

However, short-run expansions of output due to positive demand shock usually do not involve such an upgrading towards more sophisticated prod- uct. In such a case, only the variable part of labour input increases with

rm output scale, and the total employment share of white-collar workers , including both xed and variable part, decreases.

The remainder of the chapter is structured as follows: Section 2.2 shows the analytical frame work. Section 2.3 explains the data and implements empirical estimations. Section 2.4 concludes.